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Stability and bifurcation analysis in a magnetic bearing system with time delays

Author

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  • Wang, Hongbin
  • Liu, Jiaqi

Abstract

A kind of magnetic bearing system with time delay is considered. Firstly, linear stability of the model is investigated by analyzing the distribution of the roots of the associated characteristic equation. According to the analysis results, the bifurcation diagram is drawn in the appropriate parameter plane. It is found that the Hopf bifurcation occurs when the delay passes through a sequence of critical values. Then the explicit algorithm for determining the direction of the Hopf bifurcations and the stability of the bifurcating periodic solutions are derived, using the theory of normal form and center manifold. Finally, some numerical simulations are carried out to illustrate the results found.

Suggested Citation

  • Wang, Hongbin & Liu, Jiaqi, 2005. "Stability and bifurcation analysis in a magnetic bearing system with time delays," Chaos, Solitons & Fractals, Elsevier, vol. 26(3), pages 813-825.
    • Handle: RePEc:eee:chsofr:v:26:y:2005:i:3:p:813-825
    DOI: 10.1016/j.chaos.2005.03.002
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    Cited by:

    1. Jiang, Weihua & Wang, Hongbin & Wei, Junjie, 2008. "A study of singularities for magnetic bearing systems with time delays," Chaos, Solitons & Fractals, Elsevier, vol. 36(3), pages 715-719.
    2. Hu, H.Y. & Wang, Z.H., 2009. "Singular perturbation methods for nonlinear dynamic systems with time delays," Chaos, Solitons & Fractals, Elsevier, vol. 40(1), pages 13-27.
    3. Inayat-Hussain, Jawaid I., 2009. "Geometric coupling effects on the bifurcations of a flexible rotor response in active magnetic bearings," Chaos, Solitons & Fractals, Elsevier, vol. 41(5), pages 2664-2671.
    4. Li, Tzuu-Hseng S. & Kuo, Chao-Lin & Guo, Nai Ren, 2007. "Design of an EP-based fuzzy sliding-mode control for a magnetic ball suspension system," Chaos, Solitons & Fractals, Elsevier, vol. 33(5), pages 1523-1531.
    5. Ji, J.C. & Hansen, C.H., 2006. "Stability and dynamics of a controlled van der Pol–Duffing oscillator," Chaos, Solitons & Fractals, Elsevier, vol. 28(2), pages 555-570.
    6. Soni, Tukesh & Dutt, Jayanta K. & Das, A.S., 2021. "Dynamic behavior and stability of energy efficient electro-magnetic suspension of rotors involving time delay," Energy, Elsevier, vol. 231(C).
    7. Amer, Y.A. & Hegazy, U.H., 2007. "Resonance behavior of a rotor-active magnetic bearing with time-varying stiffness," Chaos, Solitons & Fractals, Elsevier, vol. 34(4), pages 1328-1345.
    8. Wang, Hongbin & Jiang, Weihua, 2006. "Multiple stabilities analysis in a magnetic bearing system with time delays," Chaos, Solitons & Fractals, Elsevier, vol. 27(3), pages 789-799.

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